Fill the sink with cold water and toss the arugula and spinach for a few minutes to clean. Spin-dry the leaves and place them in a large bowl.
In a small bowl, whisk together the lemon juice, olive oil, salt, and pepper. Pour enough dressing on the greens to moisten. Toss well.
With a very sharp knife or a vegetable peeler, shave the Parmigiano into large shards and arrange them on the arugula/spinach.